One Factor Nonparametric Tests - R

Mann-Whitney U test

• Samples: 1

• Levels: 2

• Between or Within Subjects: Between

• Reporting: “The median of ‘a’ was 13.26 (IQR = 5.01) and of ‘b’ was 14.98 (IQR = 6.19). This difference was statistically significant according to a Mann-Whitney U test (Z = -2.44, p < .05).”

# Example data
# df has subjects (S), one between-Ss factor (X) w/levels (a,b), and continuous response (Y)
df <- read.csv("data/1F2LBs.csv")
head(df, 20)

A data.frame: 20 × 3

	S	X	Y
	<int>	<chr>	<dbl>
1	1	a	14.312761
2	2	b	16.326529
3	3	a	8.113886
4	4	b	14.340093
5	5	a	13.245522
6	6	b	17.588067
7	7	a	8.889459
8	8	b	10.021004
9	9	a	13.282139
10	10	b	10.186564
11	11	a	14.295129
12	12	b	9.358157
13	13	a	8.716243
14	14	b	10.497703
15	15	a	15.976036
16	16	b	15.436113
17	17	a	13.384940
18	18	b	15.940214
19	19	a	15.292024
20	20	b	11.479020

library(coin) # for wilcox_test
df$S = factor(df$S) # Subject id is nominal (unused)
df$X = factor(df$X) # X is a 2-level factor
wilcox_test(Y ~ X, data=df, distribution="exact")

Loading required package: survival

	Exact Wilcoxon-Mann-Whitney Test

data:  Y by X (a, b)
Z = -2.4394, p-value = 0.01425
alternative hypothesis: true mu is not equal to 0

Wilcoxon Signed-Rank Test

• Samples: 1

• Levels: 2

• Between or Within Subjects: Within

• Reporting: “The median of ‘a’ was 11.92 (IQR = 2.35) and of ‘b’ was 10.74 (IQR = 2.29). This difference was statistically significant according to a Wilcoxon signed-rank test (Z = 2.11, p < .05).”

# Example data
# df has subjects (S), one within-Ss factor (X) w/levels (a,b), and continuous response (Y)
df <- read.csv("data/1F2LWs.csv")
head(df, 20)

A data.frame: 20 × 3

	S	X	Y
	<int>	<chr>	<dbl>
1	1	a	11.479751
2	1	b	10.860802
3	2	a	13.763133
4	2	b	9.609735
5	3	a	12.058958
6	3	b	9.229486
7	4	a	12.173675
8	4	b	12.112978
9	5	a	10.017150
10	5	b	10.366385
11	6	a	12.709974
12	6	b	11.641991
13	7	a	11.254307
14	7	b	9.541414
15	8	a	13.498748
16	8	b	8.973836
17	9	a	13.015273
18	9	b	8.015089
19	10	a	13.549128
20	10	b	9.171968

library(coin)
df$S = factor(df$S) # Subject id is nominal
df$X = factor(df$X) # X is a 2-level factor
wilcoxsign_test(Y ~ X | S, data=df, distribution="exact")

	Exact Wilcoxon-Pratt Signed-Rank Test

data:  y by x (pos, neg) 
	 stratified by block
Z = 2.1083, p-value = 0.03454
alternative hypothesis: true mu is not equal to 0

Kruskal-Wallis Test

• Samples: 1

• Levels: ≥2

• Between or Within Subjects: Between

• Reporting: “The median of ‘a’ was 13.96 (IQR = 5.98), of ‘b’ was 11.50 (IQR = 3.49), and of ‘c’ was 9.62 (IQR = 1.61). These differences were statistically significant according to a Kruskal-Wallis test (χ2(2, N=60) = 17.77, p < .001).”

# Example data
# df has subjects (S), one between-Ss factor (X) w/levels (a,b,c), and continuous response (Y)
df <- read.csv("data/1F3LBs.csv")
head(df, 20)

A data.frame: 20 × 3

	S	X	Y
	<int>	<chr>	<dbl>
1	1	a	16.906062
2	2	b	11.583856
3	3	c	9.821207
4	4	a	9.983235
5	5	b	12.259763
6	6	c	13.224217
7	7	a	16.168297
8	8	b	12.346154
9	9	c	10.083903
10	10	a	12.522738
11	11	b	10.437293
12	12	c	7.849846
13	13	a	14.581631
14	14	b	12.862453
15	15	c	9.060727
16	16	a	9.713943
17	17	b	11.409560
18	18	c	9.709308
19	19	a	16.478419
20	20	b	7.699005

library(coin)
df$S = factor(df$S) # Subject id is nominal (unused)
df$X = factor(df$X) # X is a 3-level factor
kruskal_test(Y ~ X, data=df, distribution="asymptotic")

	Asymptotic Kruskal-Wallis Test

data:  Y by X (a, b, c)
chi-squared = 17.767, df = 2, p-value = 0.0001387

Friedman Test

• Samples: 1

• Levels: ≥2

• Between or Within Subjects: Within

• Reporting: “The median of ‘a’ was 8.37 (IQR = 1.71), of ‘b’ was 8.97 (IQR = 2.21), and of ‘c’ was 9.97 (IQR = 3.56). These differences were statistically significant according to a Friedman test (χ2(2, N=60) = 7.90, p < .05).”

# Example data
# df has subjects (S), one within-Ss factor (X) w/levels (a,b,c), and continuous response (Y)
df <- read.csv("data/1F3LWs.csv")
head(df, 20)

A data.frame: 20 × 3

	S	X	Y
	<int>	<chr>	<dbl>
1	1	a	8.133783
2	1	b	8.862093
3	1	c	8.941638
4	2	a	8.737678
5	2	b	9.969701
6	2	c	12.963951
7	3	a	7.952228
8	3	b	7.105104
9	3	c	9.303468
10	4	a	11.941388
11	4	b	8.251948
12	4	c	9.893744
13	5	a	8.847477
14	5	b	7.753521
15	5	c	12.373811
16	6	a	8.096942
17	6	b	10.440534
18	6	c	8.758131
19	7	a	9.574017
20	7	b	9.172273

library(coin)
df$S = factor(df$S) # Subject id is nominal
df$X = factor(df$X) # X is a 3-level factor
friedman_test(Y ~ X | S, data=df, distribution="asymptotic")

	Asymptotic Friedman Test

data:  Y by X (a, b, c) 
	 stratified by S
chi-squared = 7.9, df = 2, p-value = 0.01925